Average Error: 0.6 → 0.0
Time: 1.6s
Precision: binary64
\[\frac{1}{x \cdot x}\]
↓
\[{x}^{-2} \cdot 1\]
\frac{1}{x \cdot x}
↓
{x}^{-2} \cdot 1
double code(double x) {
	return (1.0 / ((double) (x * x)));
}
↓
double code(double x) {
	return ((double) (((double) pow(x, -2.0)) * 1.0));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.2
Herbie0.0
\[\frac{\frac{1}{x}}{x}\]

Derivation

  1. Initial program 0.6

    \[\frac{1}{x \cdot x}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{1}{x}}{x}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.9

    \[\leadsto \frac{\frac{1}{x}}{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}\]

  6. Applied add-cube-cbrt1.3

    \[\leadsto \frac{\frac{1}{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\]

  7. Applied *-un-lft-identity1.3

    \[\leadsto \frac{\frac{\color{blue}{1 \cdot 1}}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\]

  8. Applied times-frac1.3

    \[\leadsto \frac{\color{blue}{\frac{1}{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \frac{1}{\sqrt[3]{x}}}}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\]

  9. Applied times-frac1.3

    \[\leadsto \color{blue}{\frac{\frac{1}{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \frac{\frac{1}{\sqrt[3]{x}}}{\sqrt[3]{x}}}\]

  10. Simplified0.9

    \[\leadsto \color{blue}{\frac{1}{x \cdot \sqrt[3]{x}}} \cdot \frac{\frac{1}{\sqrt[3]{x}}}{\sqrt[3]{x}}\]

  11. Simplified0.9

    \[\leadsto \frac{1}{x \cdot \sqrt[3]{x}} \cdot \color{blue}{\frac{1}{{\left(\sqrt[3]{x}\right)}^{2}}}\]
  12. Using strategy rm

  13. Applied add-cbrt-cube1.4

    \[\leadsto \frac{1}{x \cdot \sqrt[3]{x}} \cdot \frac{1}{\color{blue}{\sqrt[3]{\left({\left(\sqrt[3]{x}\right)}^{2} \cdot {\left(\sqrt[3]{x}\right)}^{2}\right) \cdot {\left(\sqrt[3]{x}\right)}^{2}}}}\]

  14. Simplified1.0

    \[\leadsto \frac{1}{x \cdot \sqrt[3]{x}} \cdot \frac{1}{\sqrt[3]{\color{blue}{x \cdot x}}}\]

  15. Taylor expanded around 0 0.6

    \[\leadsto \color{blue}{\frac{1}{{x}^{2}}}\]

  16. Simplified0.0

    \[\leadsto \color{blue}{{x}^{-2} \cdot 1}\]

  17. Final simplification0.0

    \[\leadsto {x}^{-2} \cdot 1\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (/ (/ 1.0 x) x)

  (/ 1.0 (* x x)))